{
  "id": 5733,
  "curve_key": "0:560406840445849470696",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-648619028293807258"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 95.55038938928844,
  "faltings_height": 6.020188358232332,
  "conductor": "34611639706896014723792957766081",
  "bad_primes": [
    "3",
    "7",
    "5189",
    "9949",
    "5426611"
  ],
  "discriminant": "-181745270149594783666445411921240371947",
  "regulator": "12518243420326925.4635140006626449879822952992968549519393735",
  "points": [
    [
      "3934177446645838/4299031489",
      "-96733182583680527330085/281874597639263"
    ],
    [
      "17842021672964194833/20605807367044",
      "-2209945792641639668289556195/93537218941279585928"
    ],
    [
      "23235877347751511128/2225100272329",
      "111973407150921272959997773930/3319130898926905733"
    ],
    [
      "3345567629221414393930/842287570440481",
      "192506511645481197142398921949878/24445030746249593713871"
    ],
    [
      "723320124292454940630681/6833178512693764",
      "615170786951062985501168838685004791/564851322388302146670088"
    ],
    [
      "6717532586850706033/5248002885904",
      "14469974664187833175570647017/12022397907178950208"
    ],
    [
      "1551087731753503720/603267550209",
      "-1894549335717685192941557789/468559716049980927"
    ],
    [
      "29653430940166268193/33934213294864",
      "27007493558697946949597243473/197677244180277618112"
    ],
    [
      "2081976720021988291761/668246799220900",
      "-93973610338910584462829074878491/17274493835855898823000"
    ],
    [
      "611094462488646392305/312101547628816",
      "14439053963257953993810100645591/5513709532623524467136"
    ],
    [
      "147054543373960235946996/19031219205079225",
      "56352367751917912970685809842668794/2625426819383449805694125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Mordell curve constructed from the Burkhardt quartic with parameters (u,v,w)=(-18/5,1/5,-10/5), specialized at t=-2182/1387. \r\n\r\nPARI/GP 2.17.4 independently returned matching computational rank bounds [11,11] for this model.",
  "created_at": "2026-10-24 17:23:37",
  "updated_at": "2026-10-24 17:23:37"
}